OFFSET
0,3
COMMENTS
Sequence found by reading the line from 0, in the direction 0, 19, ... and the parallel line from 1, in the direction 1, 54, ..., in the square spiral whose vertices are the generalized 19-gonal numbers. - Omar E. Pol, Jul 18 2012
Partial sums of A215137 (17n + 1). - Jeremy Gardiner, Aug 04 2012
REFERENCES
Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189.
Elena Deza and Michel M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6.
LINKS
Jeremy Gardiner, Table of n, a(n) for n = 0..999
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = n(17n-15)/2.
G.f.: x*(1+16*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011
a(n) = 17*n + a(n-1) - 16 (with a(0) = 0). - Vincenzo Librandi, Aug 06 2010
a(17*a(n) + 137*n + 1) = a(17*a(n) + 137*n) + a(17*n+1). - Vladimir Shevelev, Jan 24 2014
Product_{n>=2} (1 - 1/a(n)) = 17/19. - Amiram Eldar, Jan 22 2021
E.g.f.: exp(x)*(x + 17*x^2/2). - Nikolaos Pantelidis, Feb 06 2023
EXAMPLE
a(1) = 17 * 1 + 0 - 16 = 1.
a(2) = 17 * 2 + 1 - 16 = 19.
a(3) = 17 * 3 + 19 - 16 = 54. - Vincenzo Librandi, Aug 06 2010
MAPLE
MATHEMATICA
Table[(17n^2 - 15n)/2, {n, 0, 39}] (* Alonso del Arte, Feb 19 2015 *)
PROG
(PARI) a(n)=n*(17*n-15)/2; \\ Charles R Greathouse IV, Jan 24 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 15 1999
STATUS
approved